Commun. Comput. Phys., 8 (2010), pp. 701-734.


The Role of Thermodynamics in Model Reduction when Using Invariant Grids

Eliodoro Chiavazzo 1, Iliya V. Karlin 2*, Alexander N. Gorban 3

1 Aerothermochemistry and Combustion Systems Lab, ETH Zurich, 8092 Zurich, Switzerland.
2 Aerothermochemistry and Combustion Systems Lab, ETH Zurich, 8092 Zurich, Switzerland; and School of Engineering Sciences, University of Southampton, SO17 1BJ Southampton, United Kingdom.
3 Department of Mathematics, University of Leicester, LE1 7RH Leicester, United Kingdom.

Received 3 July 2009; Accepted (in revised version) 21 January 2010
Available online 17 May 2010
doi:10.4208/cicp.030709.210110a

Abstract

In the present work, we develop in detail the process leading to reduction of models in chemical kinetics when using the Method of Invariant Grids (MIG). To this end, reduced models (invariant grids) are obtained by refining initial approximations of slow invariant manifolds, and used for integrating smaller and less stiff systems of equations capable to recover the detailed description with high accuracy. Moreover, we clarify the role played by thermodynamics in model reduction, and carry out a comparison between detailed and reduced solutions for a model hydrogen oxidation reaction.

AMS subject classifications: 52B10, 65D18, 68U05, 68U07

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Key words: Chemical kinetics, model reduction, invariant manifold, entropy.

*Corresponding author.
Email: eliodoro.chiavazzo@gmail.com (E. Chiavazzo), karlin@lav.mavt.ethz.ch (I. V. Karlin), ag153@leicester.ac.uk (A. N. Gorban)
 

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